Big Omega function

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The notation Ω( ) has two meanings in mathematics:

  • f = Ω(g) means that the function f dominates g in some limit, see Big O notation.
  • Ω(n) is the total number of prime factors of n, counting prime factors with multiplicity.

If

n = \prod_{i=1}^{\omega(n)} p_i^{\alpha_i} , then \Omega(n) = \sum_{i=1}^{\omega(n)} \alpha_i.

where ω(n) is the number of distinct prime factors of n.

For example, 24 = 23.31, so: Ω(24) = 3 + 1 = 4 and ω(24) = 2.

Ω(n) for n = 1, 2, 3, ... is 0, 1, 1, 2, 1, 2, 1, 3, 2... (sequence A001222 in OEIS)

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